In this paper, we introduce a delay dependent Lyapunov equation (DDLE) approach to study
the mean square stabilization for discrete time stochastic system with both input delay and
control dependent noise. The innovative contributions of this paper are twofold. First, for a
general stochastic system with input delay and multiplicative noises, we derive a necessary
stabilizing condition based on a coupled Lyapunov equation (CLE). Second, we present a
set of necessary and sufficient stabilizing conditions for the considered stochastic system …